Hedge Ratio Calculator — Minimum-Variance, Beta, Duration, FX & Delta

Inputs & Market Data

All fields update instantly

Hedge Type

Position

Partial Hedge (%)

%

Exposure Value

$

Portfolio/asset market value

Currency

Expiry Date

For roll & margin planning

Futures/Index Price

Contract Size / Multiplier

E.g., ES multiplier=50, FX lot size in base

Initial Margin per Contract

Cost Model

bps + per contract $

Round-trip costs at trade time

Liquidity Guardrails

Max Contracts Rounding

Scenarios

Correlation Shock (Δρ)

Volatility Spike Spot (×)

Volatility Spike Hedge (×)

Spot Volatility σ_S (%)

%

Hedge Volatility σ_H (%)

%

Correlation ρ

Upload Returns CSV (Spot & Hedge)

Headers required: date, spot, hedge (returns as decimals, e.g., 0.01)

Lookback Window

Estimation

Portfolio Beta (β)

Index Level

Contract Multiplier

Portfolio DV01 ($/bp)

Futures DV01 per Contract ($/bp)

Target Hedge % of DV01

%

100% = duration neutral

FX Notional to Hedge (base)

FX Contract Size (base)

Forward Points / Carry (bps)

Net Option Delta (±)

Sum of position deltas (shares)

Underlying Price

Contract Multiplier (shares/contract)

Run Calculation

Confidence Level (VaR)

Basis Risk Add-on (bps)

Assume Positive ρ for Sign?

Results & Diagnostics

Hedge Ratio (h*)

—

Contracts / Units

—

Variance Reduction

—

vs unhedged

Margin Required

—

initial, est.

Risk Snapshot

Unhedged Volatility (σ)

—

Hedged Volatility (σ_hedged)

—

VaR Unhedged

—

VaR Hedged

—

P&L & Costs

Transaction Costs

—

Carry/Forward Impact

—

Days to Expiry

—

Charts

Rolling hedge ratio (from uploaded returns). If no data, shows a placeholder.

Volatility comparison: unhedged vs hedged.

Contract Breakdown

Hedge Type	Side	Contracts/Units	Notional per Contract	Total Notional	Initial Margin	Costs	Expiry

Save & Export

Exports include inputs, method, results, and charts for reproducibility.

Methodology & Formulas

Minimum-Variance (Futures) The hedge ratio minimizing variance is h* = ρ · σ_S / σ_H. Alternatively, regress spot returns on hedge returns; the OLS slope is a consistent estimator of h*. Contracts: N = h* · (Exposure) / (FuturesPrice · ContractSize).

Equity Beta Hedge N = β · Value / (IndexLevel · Multiplier). Short index futures to hedge a long equity portfolio (assuming positive β).

Duration/DV01 Hedge Let portfolio DV01 be D_P, futures DV01 per contract be D_F. Contracts: N = -(DV01% · D_P) / D_F, where DV01% = hedge percent.

FX Forward/Futures Units: N = (Notional% · NotionalBase) / ContractSize. Include forward points/carry as P&L impact.

Options Delta Shares to trade are -NetDelta. Contracts: N = -NetDelta / Multiplier.

Hedged Variance With spot σ_S, hedge σ_H, correlation ρ, and ratio h: Var(S − hH) = σ_S² + h² σ_H² − 2hρσ_Sσ_H. Add basis add-on if desired.